Mathematical Sciences, 2019

Siddhartha Mishra

Professor, Department of Mathematics, ETH Zürich

The Infosys Prize in Mathematics for 2019 is awarded to Prof. Siddhartha Mishra of the Swiss Federal Technical Institute of Technology at Zürich, for his outstanding contributions to Applied Mathematics, in particular for designing computational methods that solve non-linear partial differential equations arising in different areas, analyzing their effectiveness and designing algorithms to implement them.

Bio

Prof. Siddhartha Mishra received an honors degree in Mathematics and Physics from Utkal University in Bhubaneswar in 2000. After his graduation he joined the Applied Mathematics program run jointly by IISc and TIFR in Bengaluru. By 2005 he had earned both an M.S. and Ph.D. degrees from both.

Prof. Mishra went to CMA at University of Oslo as a post-doc (2005-2009) and followed it up with an Assistant Professorship at ETH Zürich (2009-2011). He returned briefly to Oslo for a year and then went back to Zürich in 2012 as an Associate Professor and became a full Professor in 2015.

Mishra is the recipient of many awards such as the Richard von Mises Prize (2015), the Jacques Louis Lions Award (2018), and the ICIAM Collatz Prize (2019). He was an invited speaker at the International Congress of Mathematicians held in Rio de Janeiro in 2018.

Scope and impact of work

The evolution of many physical phenomena are modeled mathematically by differential equations that propagate the initial data forward. The important mathematical issue is establishing the existence and uniqueness of solutions to these equations. The notion of what constitutes a solution has to be carefully formulated. Some of these questions are still unresolved.

On the other hand, in the real world one needs numerical solutions. That requires the applied mathematician to develop computational methods, i.e. algorithms that yield approximations, analyze their effectiveness, and implement them. The initial condition may not be known with any precision and one may have only statistical information about it. Sometimes the numerical calculations can even provide a clue as to the qualitative behavior of the actual solution.

Prof. Mishra has made important contributions to all these aspects of applied mathematics. He has designed stable difference schemes for approximating the solutions of hyperbolic systems of conservation laws providing some of the first examples of numerical methods for such systems with rigorous stability properties. He has provided a proof of the stability of certain common schemes used in fluid mechanics and image processing.

Mishra’s schemes are being used in astrophysics for calculations of exploding supernovas and propagation of Alfven waves in the solar chromosphere and corona and in climate studies for the simulation of the dynamics of clouds. Powerful numerical methods will continue to have a significant impact on the study of complex systems and understanding of their behavior over time.

Citation by the Jury

Many physical phenomena are modeled by some kind of fluid flow whose mathematical description involves nonlinear partial differential equations. Mathematicians prove, if they can, the existence and uniqueness of solutions to these equations. But in real life one needs numerical solutions. They involve initial data which is often not precise and perhaps only statistical in nature. One needs methods that propagate the data forward and provide an answer at the end.

The problem is often difficult because the solutions are not smooth and develop shocks that need to be tracked accurately. Such problems occur in aerodynamics, ocean waves, weather prediction, and many other areas of daily life. Prof. Mishra has made outstanding contributions by constructing numerical methods, analyzing mathematically their effectiveness and implementing them to solve concrete real-world problems.

Congratulatory message from the Jury Chair—Srinivasa S.R. Varadhan

“I want to congratulate Dr. Sid Mishra for being awarded the Infosys Prize in Mathematics this year. He has been recognized for his work in Applied Mathematics particularly his contributions to devising numerical tools for solving problems in the real world.”